Question

What is the critical angle for light to stay inside a thin glass rod (n = 1.55) surrounded by air?

____________°?

What if the rod is surrounded by water?

_________°?

Answer 1

Let’s see what happens when a light ray passes from a more optically dense medium to a less optically dense medium, at a large angle, like 50°
n i * sin θ i = n r * sin θ r
n glass = 1.55, n air = 1
1.55 * sin 50° = 1* sin θ r
sin θ r = 1.18, but the sine of an angle can not be larger than 1. So, let’s find the value of θi if sin θ r = 1
1.55* sin θ i = 1 * 1 sin θ i = 1/1.55
θ i = 40.17°

What if the rod is surrounded by water?

_________°

The index of refraction of water = 1.33

1.55 * sin θ i = 1.33 * 1
sin θ i = 1.33 / 1.55
θ i = 59° = critical angle